Protection of an electrical apparatus

ABSTRACT

An electrical apparatus configured to electrically connect to a multi-phase alternating current (AC) electrical power distribution network includes: an input electrical network including: a plurality of input nodes, each configured to electrically connect to one phase of the multi-phase AC electrical power distribution network; at least one non-linear electronic component electrically connected to the input electrical network; an impedance network electrically connected between the input electrical network and ground; and a control system configured to: access a voltage signal that represents a voltage over time at the input electrical network; determine a frequency content of the voltage signal; determine a property of the frequency content; and determine whether an input current performance condition exists in the electrical apparatus based the property of the frequency content.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. Pat. Application No.16/839,265 filed Apr. 3, 2020 and titled PROTECTION OF AN ELECTRICALAPPARATUS, which claims the benefit of U.S. Provisional Application No.62/857,611, filed on Jun. 5, 2019 and titled PROTECTION OF AN ELECTRICALAPPARATUS, each of which is incorporated herein by reference in itsentirety.

TECHNICAL FIELD

This disclosure relates to protection of an electrical apparatus, suchas a variable speed drive, an adjustable speed drive, or anuninterruptable power supply. The techniques may include, for example, aprotection module formed from electronic components and/or a method ofprotecting the electrical apparatus.

BACKGROUND

An electrical apparatus, such as a variable speed drive, an adjustablespeed drive, or an uninterruptable power supply, may be connected to analternating current (AC) high-power electrical distribution system, suchas a power grid. The electrical apparatus drives, powers, and/orcontrols a machine, or a non-machine type of load. The electricalapparatus includes an electrical network that converts AC power todirect-current (DC) power.

SUMMARY

In one aspect, an electrical apparatus configured to electricallyconnect to a multi-phase alternating current (AC) electrical powerdistribution network includes: an input electrical network including: aplurality of input nodes, each configured to electrically connect to onephase of the multi-phase AC electrical power distribution network; atleast one non-linear electronic component electrically connected to theinput electrical network; an impedance network electrically connectedbetween the input electrical network and ground; and a control systemconfigured to: access a voltage signal that represents a voltage overtime at the input electrical network; determine a frequency content ofthe voltage signal; determine a property of the frequency content; anddetermine whether an input current performance condition exists in theelectrical apparatus based the property of the frequency content.

Implementations may include one or more of the following features. Insome implementations, if an input current performance condition existsin the electrical apparatus, the control system is further configured toreduce an amount of power provided to a load that is electricallyconnected to the electrical apparatus.

In some implementations, if an input current performance conditionexists in the electrical apparatus, the control system is furtherconfigured to disconnect the electrical apparatus from the electricalpower distribution network.

The determined frequency content may include one or more harmoniccomponents of the voltage signal, and the property of the frequencycontent may include an amplitude of the one or more harmonic componentsof the voltage signal.

The determined frequency content may include one or more harmoniccomponents of the voltage signal, and the property of the frequencycontent may be a sum of values that are each based on an amplitude ofthe one or more harmonic components of the voltage signal. The propertyof the frequency content may be a total harmonic distortion.

In some implementations, to determine whether an input currentperformance condition exists based on the property of the frequencycontent, the control system is configured to compare the property of thefrequency content to a specification, and the input current performancecondition exists if the property does not meet the specification. Thecontrol system may be configured to determine more than one property ofthe frequency content, the control system may be configured to compareall of the more than one properties of the frequency content to thespecification, and the input current performance condition exists if atleast one property does not meet the specification.

The impedance network may include a plurality of impedance assemblies,and one of the impedance assemblies may be electrically connectedbetween ground and each of the plurality of input nodes, and the controlsystem being configured to accessing a voltage signal may include thecontrol system being configured to access a voltage signal at each ofthe plurality of input nodes and being configured to determine thefrequency content of the voltage signal at each of the plurality ofinput nodes. The control system may be further configured to compare thevoltage signal at each input node to the voltage signals at all of theother input nodes and to determine whether an unbalanced conditionexists based on the comparison.

The electrical apparatus may be a variable speed drive (VFD) configuredto control a torque and speed of an electric machine or anuninterruptable power supply (UPS) configured to power a non-machineload.

The at least one non-linear electrical component may be a plurality ofdiodes configured as a rectifier.

In another aspect, a method of protecting an electrical apparatus thatis electrically connected to more than one phase of a multi-phaseelectrical power distribution network includes: accessing informationrelated to an input voltage at each phase of the electrical apparatus;analyzing the information related to the input voltage at each phase todetermine a frequency content of the input voltage at each phase;determining at least one property of the frequency content of the inputvoltage at each phase; determining whether an input current performancecondition exists in the electrical apparatus based on the determined atleast one property of the frequency content of the input voltage at eachphase; and if an input current performance condition exists, reducingelectrical power provided to a load coupled to the electrical apparatusor disconnecting the electrical apparatus from the power distributionnetwork.

Implementations may include one or more of the following features. Themethod also may include comparing the information related to the inputvoltage at each phase to the information related to the input voltage ofeach of the other phases to determine whether an unbalanced conditionexists.

Determining whether an input current performance condition exists mayinclude comparing the determined at least one property for each phase toa threshold associated with that phase.

In another aspect, a multi-phase electrical apparatus, which isconfigured to electrically connect to a multi-phase AC electrical powerdistribution network and to provide a driver signal to a load, includes:an electrical network including: a plurality of input nodes, each inputnode configured to electrically connect to one phase of the multi-phaseelectrical power distribution network; and a converter configured toconvert AC electrical power to direct-current (DC) electrical power, theconverter including at least one non-linear electronic component; and animpedance network including a plurality of impedance assemblies. Eachimpedance assembly is electrically connected between one of the inputnodes and ground.

Implementations may include one or more of the following features. Themulti-phase electrical apparatus also may include a control systemconfigured to: access a voltage signal at each input node, each voltagesignal representing a voltage over time at one of the input nodes;determine a plurality of frequency representations, each frequencyrepresentation including a frequency content of one of the accessedvoltage signals; and determine whether an input current performancecondition exists in the electrical apparatus based on the frequencyrepresentations. The control system may be further configured todetermine whether an unbalanced condition exists based on the accessedvoltage signals. In some implementations, if an input currentperformance condition exists, the control system is further configuredto reduce power to the load or to disconnect the load.

Implementations of any of the techniques described herein may include anapparatus, a device, a system, and/or a method. The details of one ormore implementations are set forth in the accompanying drawings and thedescription below. Other features will be apparent from the descriptionand drawings, and from the claims.

DRAWING DESCRIPTION

FIG. 1 is a block diagram of an example of a system that includes anelectrical apparatus.

FIG. 2A is a block diagram of another example of a system that includesan electrical apparatus.

FIG. 2B is a block diagram of an example of a control system and anexample of an impedance network that may be used in the system of FIG.2A.

FIGS. 3A and 3B show examples of current drawn in each of three phasesof a load connected to, respectively, a "weak grid" and a "stiff grid."

FIGS. 4A and 4B are plots of examples of simulated data that representinput currents in each of three phases of an electrical apparatus overtime when the electrical apparatus is connected to, respectively, a"weak grid" and a "stiff grid."

FIGS. 4C and 4D are plots of examples of simulated data that representthe input voltage at each of three phases of an electrical apparatus asa function of time when the electrical apparatus is connected to,respectively, a "weak grid" and a "stiff grid."

FIGS. 4E and 4F show the input voltage in one phase of an electricalapparatus as a function of frequency when the electrical apparatus isconnected to, respectively, a "weak grid" and a "stiff grid."

FIG. 5 is a flow chart of an example process for protecting anelectrical apparatus.

FIG. 6 is a flow chart of an example process for determining whether anunbalance condition exists.

DETAILED DESCRIPTION

Referring to FIG. 1 , a block diagram of a system 100 is shown. Thesystem 100 includes an electrical apparatus 110 that is electricallyconnected to an alternating current (AC) electrical power distributionnetwork 101 and a load 102. The load 102 may be a machine or anon-machine type of load. The electrical power distribution network 101may be, for example, a multi-phase electrical power grid that provideselectricity to industrial, commercial and/or residential customers. TheAC electrical power distribution network 101 distributes AC electricalpower that has a fundamental frequency of, for example, 50 or 60 Hertz(Hz). The distribution network 101 may have an operating voltage of, forexample, up to 690 V. The network 101 may include, for example, one ormore transmission lines, distribution lines, power distribution orsubstation transformers, electrical cables, and/or any other mechanismfor transmitting electricity.

The electrical apparatus 110 includes an electrical network 112 thatreceives electrical power 105 from the distribution network 101 at aninput node 114. The electrical apparatus 110 is enclosed in a housing orenclosure 111. The housing 111 is a three-dimensional body made of asolid and rugged material that protects the electrical network 112. Theinput node 114 is accessible from an exterior of the housing 111 suchthat the electrical apparatus 110 may be connected to the distributionnetwork 101. The electrical apparatus 110 also includes an output port(not shown) that is accessible from the exterior of the housing 111. Theload 102 connects to the electrical apparatus 110 at the output port.

The electrical apparatus 110 also includes an impedance 116 that iselectrically connected to the input node 114 and to ground 113. Theground 113 is shown as a floating artificial neutral point, but may bean earth ground. The voltage across the impedance 116 is the voltage atthe input node 114. In other words, the voltage across the impedance 116is the input voltage of the electrical apparatus 110. The voltage acrossthe impedance 116 is monitored by a control system 130 and analyzed todetermine if an input current performance condition (or performancecondition) exists in the electrical apparatus 110. A performancecondition is any condition or event that negatively impacts, or couldnegatively impact, the performance of the electrical apparatus 110. Forexample, a performance condition exists when the current flowing in theelectrical network 112 has an amplitude that is capable of damaging ordegrading the electrical components in the electrical network 112.

If a performance condition is determined to exist, the control system130 takes corrective action. For example, if the current flowing in theelectrical network 112 has a peak or root-mean-square (RMS) amplitudethat could damage the components in the electrical network 112, thecontrol system 120 decreases the amount of current flowing in theelectrical network 112 or disconnects the electrical apparatus 110 fromthe distribution network 101.

The electrical network 112 includes one or more electronic componentsthat are configured to generate a driver signal 104 for the load 102based on electrical power 105 from the distribution network 101. Forexample, the electrical apparatus 110 may be a variable speed drive(VSD) or an adjustable speed drive (ASD) and the load 102 may be amachine-type load such as, for example, an induction machine, aninduction motor, or a synchronous permanent magnet machine that operatesat a speed and torque that is determined by the driver signal 104. Insome implementations, the electrical apparatus 110 is an uninterruptablepower supply (UPS) that provides electrical power to a non-machine typeof load 102, such as a lighting system. The electrical network 112includes one or more non-linear electrical components (such as diodesconfigured as a rectifier) that add harmonic components to theelectricity that flows in the electrical network 112.

The maximum amount of current that may flow at the input node 114 undershort circuit conditions is referred to as the short-circuit currentratio (SCCR) or the available fault current. The SCCR is determined bythe operating voltage and the impedance of the distribution network 101.The SCCR may be, for example, 5 kilo-Amperes (kA) or 100 kA. The SCCRincreases as the impedance of the distribution network 101 decreases. Apower distribution network that has a relatively low impedance may bereferred to as a "stiff grid" and a power distribution network that hasa relatively high impedance may be referred to as a "weak grid." Thus,the SCCR of a "stiff grid" is greater than the SCCR of a "weak grid."The impedance of the distribution network 101 is represented by aninductance (Ls) in series with a resistance (Rs). For example, for avariable speed drive (VFD) rated as 60 horsepower (HP) (~45 kW), 480 V,3 \-phase input, 60 Hz, the "weak grid" input impedance at 5 kA SCCR hasLs = 104 micro-henries (µH) and Rs = 39 milli-ohms (m'Ω). The "stiffgrid" input impedance at 100 kA SCCR has Ls = 7.2 µH and Rs = 543 µὩ.

The SCCR may impact the performance of the electrical network 112 and,thus, may impact the performance of the electrical apparatus 110. Forexample, in implementations in which the distribution network 101 is a"stiff grid," the electrical network 112 may be exposed to excessiveinput electrical currents even when the load 102 is operating undernormal load conditions. The exposure to high electrical currents maycause the components of the electrical network 112 to overheat, whichmay lead to the components malfunctioning, failing, or degrading. Someprior systems have included an additional impedance (such as a linereactor, input inductors, or a DC choke) in series with the impedance ofthe distribution network 101 to limit or prevent current spikes andcurrent surges. However, such additional impedances increase overallcosts, require additional space, generate heat, and waste electricity.

On the other hand, the electrical apparatus 110 includes the impedance116 that is electrically connected to the input node 114 and to ground113. Unlike the line impedance of the prior systems, current flowinginto the electrical apparatus 110 does not flow in the impedance 116 andthe impedance 116 is not part of the impedance of the distributionnetwork 101. The impedance 116 allows the voltage at the input node 114to be monitored easily and without interfering with the operation of theelectrical apparatus 110. The impedance 116 may be made from, forexample, simple and inexpensive components such as surface mountresistors.

The control system 130 uses properties of the monitored voltage todetermine whether or not a performance condition exists in theelectrical apparatus 110. For example, the control system 130 mayanalyze harmonics in the monitored voltage to determine whether or notexcessive currents are flowing in the electrical network 112. Ifdamaging or potentially damaging conditions exist, the control system130 may remove the electrical apparatus 110 from service or reduce thestress on the electrical apparatus 110 by, for example, temporarilyreducing the amount of current the electrical apparatus 110 provides tothe load 102. The impedance 116 and the control system 130 protect theelectrical apparatus 110 without relying on current sensors (which maybe expensive and/or inconvenient to use) and without adding additionalimpedances into the path of the distribution network 101.

FIG. 2A is a schematic of a system 200. The system 200 includes anelectrical apparatus 210 that is connected to a three-phase ACelectrical power distribution network 201 and a load 202. The load 202may be a machine or non-machine type load. For example, in someimplementations, the electrical apparatus 210 is a VFD that controls amachine 202, such as, for example, an induction motor or a permanentmagnet synchronous machine. In other implementations, the electricalapparatus 210 is a UPS that controls a non-machine type load, such as,for example, a lighting system.

The electrical apparatus 210 receives three-phase electrical power fromthe distribution network 201 and provides a three-phase driver signal204 to the load 202. The electrical apparatus 210 includes a controlsystem 230 that monitors a voltage at an impedance network 216 and usesthe monitored voltage to assess whether or not a performance conditionexists in the electrical apparatus 210. The dashed lines in FIG. 2A areused to show groupings of elements, and the dashed lines do notnecessarily represent physical objects. However, the electricalapparatus 210 may include an enclosure similar to the housing 111 (FIG.1 ). In implementations that include an enclosure, the impedance network216 may be within the enclosure.

FIG. 2B is a block diagram of the control system 230 and the impedancenetwork 216. FIGS. 3A and 3B show examples of current drawn by the sameload for, respectively, a "weak grid" and a stiff grid." FIGS. 4A-4Fshow simulated data related to the input conditions of the electricalapparatus 210. FIGS. 2A, 3A, 3B, and 4A-4F are discussed prior todiscussing FIG. 2B in more detail.

The electrical power distribution network 201 distributes AC electricalpower that has a fundamental frequency of, for example, 50 or 60 Hertz(Hz). The distribution network 201 may have an operating voltage of upto 690 V. The distribution network 201 may include, for example, one ormore transmission lines, distribution lines, electrical cables, and/orany other mechanism for transmitting electricity. The distributionnetwork 201 includes three phases, which are referred to as a, b, and c.Each phase has a respective voltage ea, eb, ec. The impedance of thedistribution network 201 is represented by an inductor Ls in series witha resistance Rs. The impedance of the distribution network 201 dependson the impedance characteristics of the components included in thedistribution network 201.

The electrical apparatus 210 includes input nodes 214 a, 214 b, 214 c,each of which is electrically coupled to one of the three phases of thedistribution network 201. In the example of FIG. 2A, the input node 214a is electrically connected to the a phase, the input node 214 b iselectrically connected to the b phase, and the input node 214 c iselectrically connected to the c phase. The electricity provided by thedistribution network 201 is nominally sinusoidal and includes only asingle frequency component at the fundamental frequency. The expected,theoretical, or nominal current provided by distribution network 201 isthe same for the "weak grid" and the "stiff grid."

The electrical apparatus 210 includes an electrical network 212. Theelectrical network 212 includes a rectifier 217, a DC link 218, and aninverter 219. The rectifier 217 shown in FIG. 2A is a three-phasesix-pulse bridge that includes six electronic switches. In the exampleof FIG. 2A, the six electronic switches are diodes D1-D6. Each diodeD1-D6 includes a cathode and an anode and is associated with a forwardbias voltage. Each diode D1-D6 allows current to flow in the forwarddirection (from the anode to the cathode) when voltage of the anode isgreater than the voltage of the cathode by at least the bias voltage.When the voltage difference between the anode and the cathode is lessthan the forward bias voltage, the diode does not conduct current in theforward direction.

The input node 214 a is electrically connected to the anode of the diodeD1 and the cathode of the diode D4. The input node 214 b is electricallyconnected to the anode of the diode D3 and the cathode of the diode D6.The input node 214 c is electrically connected to the anode of the diodeD5 and the cathode of the diode D2. The diodes D1-D6 rectify the inputcurrents ia, ib, ic into a DC current id.

The diodes D1-D6 are also electrically connected to the DC link 218. Thecathode of each diode D1, D3, D5 is electrically connected to the DClink 218, and the anode of each diode D2, D4, D6 is electricallyconnected to the DC link 218. The DC link 218 includes a capacitornetwork C. The rectified current id flows into the capacitor network Cand is stored. The capacitor network C includes one or more capacitorsthat store electrical energy when the rectified current id flows fromthe rectifier 217 and discharge the stored electrical energy when therectified current id does not flow from the rectifier 217.

The inverter 219 converts the DC power stored in the capacitor network Cinto three-phase AC driver signal 204 that is provided to the load 202.The three-phase driver signal 204 has phase components 204 u, 204 v, 204w, each of which is provided to one of the three-phases of the load 202.The inverter 219 includes a network of electronic switches SW1-SW6 thatare arranged to generate the driver signal 204. Each of the switchesSW1-SW6 may be, for example, a power transistor. Because the inverter219 uses the electrical energy stored in the DC link 218, the driversignal 204 continues to be produced as expected and load 202 mayfunction under normal and expected load conditions even if the magnitudeof the current that flows in the rectifier 217 and into the DC link 218increases to a level that may damage the components in the rectifier 217and the DC link 218.

FIG. 3A shows an example the current drawn by each phase u, v, w of theload 202 as a function of time in an implementation in which thedistribution network 201 is a "weak grid" with a SCCR of 5 kA and afundamental frequency of 60 Hz. FIG. 3B is an example of current drawnby each phase u, v, w of the load 202 in an implementation in which thedistribution network is a "stiff grid" with a SCCR of 100 kA and afundamental frequency of 60 Hz. In FIGS. 3A and 3B, the u phase currentis plotted with a solid line style, the v phase current is plotted witha dashed line style, and the w phase current is plotted with a dash-dotline style. In FIGS. 3A and 3B, the current drawn by each phase of theload 202 lags or leads the current in the other two phases by 120degrees (°).

In both FIGS. 3A and 3B, the electrical apparatus 210 was a 60 HP (~45kW), 480 V, 3 \-phase input, 60 Hz VFD that includes an electricalnetwork such as the electrical network 212 and the load 202 was a ratedinduction machine load of 250 Newton-meters (Nm). The currents drawn bythe load 202 are the same for the "stiff grid" and the "weak grid," andthe currents drawn by the load 202 are nearly sinusoidal. Even thoughthe currents drawn by the load 202 are the same for the "stiff grid" andthe "weak grid," the currents flowing at the input nodes 214 a, 214 b,214 c are not the same for the "stiff grid" and the "weak grid," asdiscussed below.

FIGS. 4A-4F are plots of example input current or voltage data producedby a simulation in which the fundamental frequency of the electricaldistribution network 201 was 60 Hz. In the examples of FIGS. 4A-4F, theelectrical apparatus 210 was a 60 HP (~45 kW), 480 V, 3 \-phase input,60 Hz VFD that includes an electrical network such as the electricalnetwork 212. 4A and 4B are plots of simulated data that represent theinput currents ia, ib, ic over time. FIGS. 4C and 4D are plots ofsimulated data that represent the input voltage at any of the inputnodes 214 a, 214 b, 214 c as a function of time. FIGS. 4E and 4F showthe input voltage at any of the input nodes 214 a, 214 b, 214 c as afunction of frequency. The data shown in FIGS. 4A-4F is discussed below.

FIG. 4A shows the simulated input currents ia, ib, ic in animplementation in which the distribution network 201 has a SCCR of 5 kA.FIG. 4B show the simulated input currents ia, ib, ic in animplementation in which the distribution network 201 has a SCCR of 100kA. In FIGS. 4A and 4B, ia is plotted with a dash-dot-dash-dash linestyle, ib is plotted with a dashed line style, and ic is plotted with adotted line style. Each diode D1-D6 conducts electrical current when thevoltage of the anode is greater than the voltage of the cathode by atleast the forward bias voltage. Thus, the state of the diodes D1 and D4depends on the voltage of the input node 214 a and the voltage at the DClink 218. The state of the diodes D3 and D6 depends on the voltage atthe input node 214 b and the voltage at the DC link 218. The state ofthe diodes D5 and D2 depends on the voltage of the input node 214 c andthe voltage at the DC link 218. The input currents ia, ib, ic flow onlywhen the input voltage is greater than the DC voltage at the DC link218. As a result, the input currents ia, ib, ic vary in time as shown inFIGS. 4A and 4B.

As shown in FIGS. 4A and 4B, the magnitude of the input currents ia, ib,ic is greater in the 100 kA SCCR scenario (FIG. 4B) than in the 5 kASCCR scenario (FIG. 4A). The data shown in FIGS. 4A and 4B is for a 60HP (~45 kW), 480 V, 3 \-phase input, 60 Hz VFD that includes anelectrical network such as the electrical network 212. In the 5 kA SCCRscenario at the rated induction machine load of 250 Newton-meters (Nm),the peak input current in 210 was 168 A and the root mean square (RMS)current was 80 A. In the 100 kA scenario at the rated induction machineload of 250 Nm, the peak input current was 374 A and the RMS current was121 A.

Thus, for the same load conditions, the peak input current and the RMScurrent that flows in the input nodes 214 a, 214 b, 214 c is higher forthe 100 kA (the "stiff grid") scenario than for the 5 kA scenario (the"weak grid"). As the SCCR increases, the magnitude of the current thatflows in the rectifier 217 increases due to smaller voltage drops acrosssmaller Ls and Rs. As a result, more electrical energy flows into and isstored by the capacitors C, and the voltage at the DC link 218increases. The voltage ripple containing harmonics at the DC link 218increases, which adds thermal stress to the DC link capacitors. Thethermal stress degrades the DC link capacitors, shortening theirlifetimes and decreasing their reliability. In addition, the much higherpeak and RMS input currents ia, ib, ic for the 100 kA SCCR scenario(FIG. 4B) can exceed each semiconductor device peak current and RMScurrent ratings in the rectifier bridge 217, adding stress and causingfailures. The input currents ia, ib, ic for the 100 kA SCCR scenario(FIG. 4B) also have shorter temporal durations than in the 5 kA SCCRscenario (FIG. 4A). This is because the time during which any of thediodes D1-D6 conduct current decreases because the voltage at the DClink 218 is greater. Higher currents flow in the input nodes 214 a, 214b, 214 c as the SCCR increases and the impedance (Ls and Rs) decreases,even though the current drawn by the load 202 stays the same (forexample, as shown in FIGS. 3A and 3B). The higher currents have thepotential to damage the electronic components in the rectifier 217 andthe DC link 218.

FIGS. 4C and 4D show simulated input voltage as a function of time. FIG.4C includes a plot 460 that shows simulated input voltage as a functionof time for the scenario in which the electrical apparatus 210 isconnected to a 5 kA SCCR distribution network 101. FIG. 4D includes aplot 462 that shows simulated input voltage as a function of time forthe scenario in which the electrical apparatus 210 is connected to a 100kA SCCR distribution network 201. The plots 460 and 462 may be thevoltage as a function of time at any one of the input nodes 214 a, 214b, 214 c. In other words, each of the plots 460 and 462 show the inputvoltage of one phase as a function of time. FIGS. 4C and 4D also includea plot 464 that shows the nominal sinusoidal voltage of one phase of thedistribution network 201 (ea, eb, or ec) without any distortion.

The plots 460 and 462 deviate from the nominal sinusoidal voltage 464from the distribution network 201 because of the current peaks drawn bythe electrical apparatus 210. The deviations from the nominal sinusoidalvoltage is distortion. The current peaks and non-linear characteristicsof the current drawn by the electrical apparatus 210 are shown in FIGS.4A and 4B. Due to the current peaks and the discontinuous conduction,the input voltage at the electrical apparatus 210 (the voltage at any ofthe input nodes 214 a, 214 b, 214 c) includes frequencies other than thefundamental frequency and the input voltage is not a pure sinusoidalwaveform. The frequencies other than the fundamental frequency producethe distortion shown in FIGS. 4C and 4D. The distortion is greater inthe 5 kA scenario (FIG. 4C) than the 100 kA scenario (FIG. 4D) becausethe values of Ls and Rs are larger in the 5 kA scenario.

The input voltage waveforms in FIGS. 4C and 4D represent one of thethree phases. For balanced three phases (when the voltage is the same ineach phase), the distortion levels are the same in each phase. But forunbalanced input voltages, the distortion levels and amplitudes can bedifferent in each phase. The harmonic characteristics can be used fordetecting the voltage unbalanced condition and protecting the systemfrom premature failures.

FIG. 4E shows the simulated input voltage data plotted as 460 in FIG. 4Cas a function of frequency. FIG. 4F shows the simulated input voltagedata plotted as 462 in FIG. 4D as a function of frequency. The datashown in each of FIGS. 4E and 4F is a voltage spectrum that shows thespectral or frequency content of the input voltage of the electricalapparatus 210. The fundamental frequency component is labeled as thecomponent 465. In addition to the fundamental frequency, the inputvoltages include higher-order frequency components or harmonics. In thescenario in which the electrical apparatus 210 is connected to a 5 kASCCR network (FIG. 4E), the amplitude of the fifth and seventh harmonicsare greater than 10 times larger than the amplitude of the fifth andseventh harmonics in the scenario in which the electrical apparatus 210is connected to a 100 kA SCCR network (FIG. 4F). Thus, for the same loadconditions, analysis of the amplitude of the voltage harmonics revealswhether the electrical apparatus 210 is connected to a "weak grid" or a"strong grid." The fifth and seventh harmonics are labeled as 468 inFIG.4E and 469 in FIG. 4F.

Referring to FIG. 2B, the control system 230 and the impedance network216 are shown. The control system 230 is an example of an implementationof the control system 130 of FIG. 1 . The control system 230 analyzesvoltages in the impedance network 216 to determine whether or not aperformance condition exists in the electrical apparatus 210. Aperformance condition exists, for example, when the currents ia, ib, icare damaging or potentially damaging to the components in the rectifier217 and/or DC link 218.

The impedance network 216 includes an impedance apparatus for each phaseof the distribution network 101 that is electrically connected to theelectrical apparatus 210. Thus, in the example of FIG. 2B, the impedancenetwork 216 includes three impedance apparatuses or protection modules216 a, 216 b, 216 c. The impedance apparatuses 216 a, 216 b, 216 c areconnected between respective input nodes 214 a, 214 b, 214 c andrespective grounds 213 a, 213 b, 213 c. The voltages labeled Va, Vb, Vc(FIG. 2B) are the input voltages at the respective input nodes 214 a,214 b, 214 c. The grounds 213 a, 213 b, 213 c are shown as floatingartificial neutral points and are not necessarily the same point. Insome implementations, the grounds 213 a, 213 b, 213 c are connected toearth ground.

Each impedance apparatus 216 a, 216 b, 216 c includes a respectivevoltage sensor 231 a, 231 b, 231 c. The voltage sensors 231 a, 231 b,231 c may be, for example, potentiometers. Each of the impedances 216a-216 c also includes a capacitor C1 and a voltage divider formed byresistors R1 and R2. The capacitor C1 is in parallel with the resistorR2. The voltage sensors 231 a, 231 b, 231 c measure the voltage acrossthe resistor R2 in each of the impedance apparatus 216 a, 216 b, 216 c,respectively, and provide data representing the measured voltage to thecontrol system 230. The resistors R1 and R2 and the capacitor C1 may be,for example, surface mount components that are suitable for mounting ona printed circuit board (PCB).

In the example shown in FIG. 2B, each impedance apparatus 216 a, 216 b,216 c includes the resistors for R1 and R2 in the same configuration.However, in other implementations, each impedance apparatus 216 a, 216b, 216 c may have a different configuration and may include differentcomponents. Moreover, any of the impedance apparatus 216 a, 216 b, 216 cmay have a different configuration than the configurations shown in FIG.2B. The impedance apparatus 216 a, 216 b, 216 c may be implemented inany sort of topology with any electronic components that form a knownimpedance such that data from the voltage sensors 231 a, 231 b, 231 cmay be used to determine the voltages at the respective input nodes 214a, 214 b, 214 c,

The control system 230 includes an electronic processing module 232, asignal processing module 233, an electronic storage 234, and aninput/output (I/O) interface 236. The electronic processing module 232includes one or more electronic processors. The electronic processors ofthe module 232 may be any type of electronic processor and may or maynot include a general purpose central processing unit (CPU), a graphicsprocessing unit (GPU), a microcontroller, a field-programmable gatearray (FPGA), Complex Programmable Logic Device (CPLD), and/or anapplication-specific integrated circuit (ASIC).

The signal processing module 233 is configured to transform dataproduced by the sensors 231 a, 231 b, 231 c and/or data based on dataproduced by the sensors 231, 231 b, 231 c between a time domain and afrequency domain. The signal processing module 233 may be implemented inhardware or software, or in a combination of hardware and software. Forexample, the signal processing module 233 may be a collection ofinstructions that are stored on the electronic storage 234 thatcollectively form a function or subroutine that the electronicprocessing module 232 may execute to perform a fast Fourier transform(FFT). In other implementations, the signal processing module 233 isimplemented with a collection of electronic components that form, forexample, a phase-locked loop or other configuration that is capable ofextracting certain frequencies from an input signal.

The electronic storage 234 may be any type of electronic memory that iscapable of storing data and instructions in the form of computerprograms or software, and the electronic storage 234 may includevolatile and/or non-volatile components. The electronic storage 234 andthe processing module 232 are coupled such that the processing module232 is able to access or read data from and write data to the electronicstorage 234. The electronic storage 234 stores instructions that, whenexecuted, cause the electronic processing module 232 to analyze dataand/or retrieve information. The electronic storage 234 also may storeinformation about the system 200. For example, the electronic storage234 may store information about the impedance network 216 for use in,for example, analyzing data from the sensors 231 a, 231 b, 231 c. Thestored information about the impedance network 216 may include values ofthe resistors R1 and R2.

The I/O interface 236 may be any interface that allows a human operatorand/or an autonomous process to interact with the control system 230.The I/O interface 236 may include, for example, a display (such as aliquid crystal display (LCD)), a keyboard, audio input and/or output(such as speakers and/or a microphone), visual output (such as lights,light emitting diodes (LED)) that are in addition to or instead of thedisplay, serial or parallel port, a Universal Serial Bus (USB)connection, and/or any type of network interface, such as, for example,Ethernet. The I/O interface 236 also may allow communication withoutphysical contact through, for example, an IEEE 802.11, Bluetooth, or anear-field communication (NFC) connection. The control system 230 maybe, for example, operated, configured, modified, or updated through theI/O interface 236.

The I/O interface 236 also may allow the control system 230 tocommunicate with components in the system 200 and with systems externalto and remote from the system 200. For example, the I/O interface 236may control a switch or a switching network (not shown) or a breakerwithin the system 200 that allows the electrical apparatus 210 to bedisconnected from the distribution network 210. In another example, theI/O interface 236 may include a communications interface that allowscommunication between the control system 230 and a remote station (notshown), or between the control system 230 and a separate monitoringapparatus. The remote station or the monitoring apparatus may be anytype of station through which an operator is able to communicate withthe control system 230 without making physical contact with the controlsystem 230. For example, the remote station may be a computer-based workstation, a smart phone, tablet, or a laptop computer that connects tothe motor control system 230 via a services protocol, or a remotecontrol that connects to the control system 230 via a radio-frequencysignal.

Referring to FIG. 5 , a flow chart of a process 500 is shown. Theprocess 500 is an example of a process for protecting an electricalapparatus, such as, for example, a VFD or a UPS. The process 500 may beperformed by the signal processing module 233 and/or one or moreelectronic processors in the electronic processing module 232 (FIG. 2B).The process 500 is discussed with respect to the system 200 of FIG. 2 .However, the process 500 may be performed with other systems. Forexample, the process 500 may be performed with the system 100 of FIG. 1.

Information related to an input voltage at each phase of the electricalapparatus 210 is accessed (510). For example, each of the voltagesensors 231 a, 231 b, 231 c measures the voltage across the resistor R2of the respective impedance apparatus 216 a, 216 b, 216 c. The voltageacross each resistor R2 is information related to the voltage at therespective input node 214 a, 214 b, 214 c according to Equation 1:

$V_{R2} = V_{i}\left( \frac{R2}{R1 + R2} \right)$

where V_(R2) is the voltage across the resistor R2 as measured by one ofthe sensors 231 a, 231 b, 231 c and V_(i) is the voltage at therespective input node 214 a, 214 b. 214 c. The information may beaccessed by the control system 230 receiving data that represents thevoltage measured by each sensor 231 a, 231 b, 231 c. For example, thevoltage sensors 231 a, 231 b, 231 c may provide information related tothe measured voltage to the control system 230. In another example, thecontrol system 230 may retrieve the measured voltage from the sensors231 a, 231 b, 231 c.

The temporal characteristics of the input voltage at the input nodes 214a, 214 b, 214 c are determined from voltage measurements obtained fromthe voltage sensors 231 a, 231 b, 231 c. For example, measurements fromeach of the voltage sensors 231 a, 231 b, 231 c obtained at differenttimes are stored on the electronic storage 234. The electronic storage234 also may store a collection of instructions, for example, a computerprogram, that determines the voltage at each input node 214 a, 214 b,214 c over time based on the measured voltage data, stored values for R1and R2, and Equation 1. The voltage at each input node 214 a, 214 b, 214c as a function of time is referred to, respectively, as Vta, Vtb, Vtc.As discussed above, the plots 460 (FIG. 4C) and 462 (FIG. 4D) showexamples of a voltage at one of the input nodes 214 a, 214 b, 214 c as afunction of time. One of the voltages Vta, Vtb, Vtc may be similar tothe voltages shown in the plot 460 (FIG. 4C) or the plot 462 (FIG. 4D).Each of the voltages Vta, Vtb, Vtc are separated by 120° in phase. In abalanced voltage scenario (discussed below with respect to (515)), eachof the voltages Vta, Vtb, Vtc has the same or substantially the samedistortion. In an unbalanced voltage scenario, each of the voltages Vta,Vtb, Vtc has a different distortion.

In some implementations, the process 500 analyzes the input voltageinformation to determine whether an unbalanced condition exists (515).FIG. 6 is a flow chart of the process 515 that may be used to determinewhether an unbalanced condition exists. The process 515 determineswhether the electrical apparatus 210 is balanced or unbalanced. If theelectrical apparatus 210 is balanced, then the electrical apparatus 210is operating in Category 1. If the electrical apparatus 210 isunbalanced, and is operating in Category 2 or 3, as discussed below. Insome implementations, the process 515 is not performed and the process500 continues to (520). In these implementations, the electricalapparatus 210 is assumed to be in Category 1.

Referring to FIG. 6 , an unbalanced metric is determined (680). Theunbalanced metric is based on the input voltage as a function of time ateach of the input nodes 214 a, 214 b, 214 c (respectively Vta, Vtb,Vtc). As discussed above, the input voltage as a function of time ateach input node 214 a, 214 b, 214 c is obtained at (510). When the inputvoltage is balanced, the voltage over time at each input node 214 a, 214b, 214 c (respectively, Vta, Vtb, Vtc) is the same, although the phasesare separated from each other by 120°. When the input voltage isunbalanced, the voltage over time at each input node 214 a, 214 b, 214 c(respectively, Vta, Vtb, Vtc) is not the same. In other words, when theinput voltage is balanced, the RMS voltage is the same at each inputnode 214 a, 214 b, 214 c. When the input voltage is unbalanced, the RMSvoltage is not the same at each input node 214 a, 214 b, 214 c. Theunbalanced metric is any quantity that characterizes the discrepancyamong the input voltages as a function of time at the input nodes 214 a,214 b, 214 c. The unbalance metric may be, for example, an unbalancepercentage. The unbalance percentage for a three-phase system such asthe electrical apparatus 210 is determined, for example, using Equations(2) and (3):

$Unbalance\mspace{6mu} percentage\mspace{6mu}\mspace{6mu} = \mspace{6mu}\mspace{6mu}\frac{\left| {V_{avg} - V_{\varphi}} \right|}{V_{avg}}$

$V_{avg}\,\, = \mspace{6mu}\mspace{6mu}\frac{V_{ar} + V_{br} + V_{cr}}{3}$

where Var, Vbr, Vcr are the RMS amplitudes of the voltages as a functionof time at the input nodes 214 a, 214 b, 214 c, respectively; Vavg isthe average of the RMS amplitude of the voltages as a function of timeat the input nodes 214 a, 214 b, and 214 c; and Vφ is the amplitude ofthe one of the three input phase RMS voltages Var, Vbr, Vcr thatproduces the largest deviation from the average RMS voltage Vavg. Whenthe voltages as a function of time at the input nodes 214 a, 214 b, 214c are balanced, the unbalance percentage given by Equations (2) and (3)is zero (0). The unbalance percentage increases as the unbalance becomesmore severe.

Whether or not an unbalanced condition exists is determined based on theunbalance metric (682). For example, the unbalance metric determined in(680) is compared to a first unbalanced threshold value that is storedon the electronic storage 234. If the unbalance metric is less than thefirst unbalanced threshold, the input voltages at the input nodes 214 a,214 b, 214 c are balanced and an unbalanced condition does not exist.This is referred to as a Category 1 scenario. A flag or variable thatindicates that the input voltages are balanced and that a Category 1scenario exists is set (683) and is stored in the electronic storage 234and/or returned to the process 500. The process 515 ends and the process500 continues to (520).

On the other hand, if the unbalance metric is greater than the firstunbalanced threshold, then an unbalanced condition exists, and the inputvoltages at the input nodes 214 a, 214 b, 214 c are considered to beunbalanced. If an unbalanced condition exists, then the severity of theunbalance is assessed by determining whether a single-phase conditionexists (684).

The unbalanced input voltage may lead to damage and/or a shortening ofthe lifetime of the capacitor network C in the DC link 218. For example,a relatively small amount of voltage unbalance may lead to one of theinput nodes 214 a, 214 b, 214 c conducting much more current than theother input nodes. For example, a much higher current may flow in one ofthe input nodes 214 a, 214 b, 214 c than the other nodes during anunbalanced condition. The high amount of current may damage theelectrical components in the rectifier 217 and/or the voltage andcurrent harmonics on the DC link may damage the capacitors in thecapacitor network C.

If the unbalanced condition is severe, the electrical apparatus 210 mayenter single-phase operation. In single-phase operation, only two of theinput nodes 214 a, 214 b, 214 c are connected to the power distributionnetwork 201. Two of the three input nodes conduct all of the inputcurrent for the electrical apparatus 210, and this leads to even greaterdamage of the electrical components in the network 212. Whether or notthe electrical apparatus 210 has entered single-phase operation isdetermined (684). To determine whether the electrical apparatus 210 isin single-phase operation, the unbalance metric is compared to a secondunbalance threshold. The second unbalance threshold is greater than thefirst unbalance threshold. Thus, the second unbalance threshold is usedto detect a more severe unbalance condition that is negatively affectingthe performance of electrical apparatus 210.

If the electrical apparatus 210 is not in single-phase operation, asingle-phase condition does not exist (but an unbalance condition existsbased on (682)), and a Category 2 scenario exists. A flag or variablethat indicates that the input voltages are unbalanced and that aCategory 2 scenario exists is set (685) and is stored in the electronicstorage 234 and/or returned to the process 500. The process 520 ends.

If the electrical apparatus 210 is in single-phase operation, a Category3 scenario exists. A flag or variable that indicates that the inputvoltages are severely unbalanced and that a Category 3 scenario existsis set (686) and is stored in the electronic storage 234 and/or returnedto the process 500. The process 515 ends.

Referring again to FIG. 5 , the process 500 continues at (520). At(520), the input voltage information obtained at (510) is analyzed todetermine frequency content of the input voltage. The input currents ia,ib, ic include components at the fundamental frequency of thedistribution network 201 and components at harmonics of the fundamentalfrequency. Thus, the input voltage at each of the input nodes 214 a, 214b, 214 c as a function of time (Vta, Vtb, Vtc, respectively) alsoinclude components at the fundamental frequency and components atharmonics of the fundamental frequency. A harmonic is a component thathas a frequency that is an integer multiple of the fundamentalfrequency. The frequency component at the fundamental frequency is alsoreferred to as the first harmonic. Other harmonics have higherfrequencies that are determined by the multiple associated with thatharmonic. For example, in implementations in which the distributionnetwork 201 has a fundamental frequency of 60 Hz, the third harmonic isat 180 Hz, and the fifth harmonic is at 300 Hz.

In some implementations, the frequency content of Vta, Vtb, Vtc isdetermined with a signal processing technique. For example, theelectronic storage 234 stores instructions that transform the voltagesVta, Vtb, Vtc (which are a function of time) into voltages that are afunction of frequency. The voltages Vta, Vtb, Vtc may be transformedinto three separate signals Vfa, Vfb, Vfc, each of which are infrequency domain by, for example, applying the Fourier transform to eachvoltage signal Vta, Vtb, Vtc. Each signal Vfa, Vfb, Vfc provides theamplitude of the voltage as a function of frequency. The voltagespectrums shown in FIGS. 4E and 4F are examples of information that maybe included in each of the signals Vfa, Vfb, Vfc. The voltage spectrumsshown in FIGS. 4E and 4F are provided only as examples. The specificcharacteristics of the signals Vfa, Vfb, Vfc depend on thecharacteristics of the distortion in the respective phase a, b, c.

In some implementations, the frequency content of the input voltageinformation is determined by extracting the fundamental component andone or more other harmonics. The fundamental harmonic and anotherharmonic component h may be extracted using the following examplerelationships with h=3:

$\begin{array}{l}{\frac{1}{2\pi}{\int_{0}^{2\pi}{\left( {I_{1}cos\theta + I_{3}cos3\theta} \right)cos3\theta d\theta = \frac{I_{3}}{2}}}} \\ \\{\mspace{6mu}\mspace{6mu}\mspace{6mu}\mspace{6mu}\mspace{6mu}\frac{1}{2\pi}{\int_{0}^{2\pi}{\left( {I_{1}cos\theta + I_{3}cos3\theta} \right)sin3\theta d\theta = 0}}}\end{array}$

where I₁ is the amplitude of the fundamental component, I₃ is theamplitude of the 3^(rd) harmonic component, θ = ωt, ω = 2πf, and f isthe fundamental frequency. In these implementations, instructions thatimplement Equation 4 are stored on the electronic storage 234 and areexecuted by the electronic processing module 232.

The examples above relate to the control system 230 using softwarestored on the electronic storage 234 to transform the input voltagesignals Vta, Vtb, Vtc into the frequency domain input voltage signalsVfa, Vfb, Vfc. However, other approaches are possible. For example, thecontrol system 230 may implement the signal processing module 231 as aphase-locked loop as part of digital or analog electronic network thatextracts particular frequencies from voltage signals measured by thesensors 231 a, 231 b, 231 c.

At least one property of the frequency content is determined (530). Theproperty of the frequency content may be, for example, an amplitude ofone of more of the harmonics in each of the frequency domain voltagesignals Vfa, Vfb, Vfc. For example, the amplitude of the fifth, seventh,eleventh, and thirteenth harmonics may be determined. The amplitudes maybe determined using the example formulation shown in Equation (4) or byapplying a transformation such as the Fourier transform to time-domainvoltage data and then identifying the amplitude at the frequenciesassociated with the harmonic or harmonics of interest.

In some implementations, the property of the frequency content is atotal harmonic distortion (THD). The THD is the ratio of square root ofthe sum of the powers of all harmonic components to the power of thefundamental frequency. The THD may be determined using:

$THD\,\, = \,\,\frac{\sqrt{V_{2}^{2} + V_{3}^{2} + V_{4}^{2}\mspace{6mu}\ldots}}{V_{1}}$

where Vn is the amplitude of the nth harmonic and n=1 is the fundamentalfrequency.

In some implementations, the one or more frequency-based properties aredetermined for the frequency content of each phase of the input voltage.In these implementations, one or more properties of each the frequencydomain voltage signals Vfa, Vfb, and Vfc are determined. For example, aTHD may be determined for each phase and/or an amplitude of one or moreharmonics may be determined for each phase. In another example, theamplitude of each of a plurality of harmonics is determined in eachphase.

In other implementations, the frequency-based properties are determinedfor fewer than all of the phases. For example, if a balanced conditionexists (Category 1) as determined by (515), the frequency content is thesame for all of the phases. In some implementations, if a balancedcondition exists, the frequency-based properties may be determined forfewer than all of the phases.

Whether or not a performance condition exists is determined based on theone or more properties of the frequency content (540). A performancecondition is a condition that is or could negatively impact theperformance of the electrical apparatus 210. Excessive currents flowingin the rectifier 217 and/or the DC link 218 are an example of aperformance condition. Excessive currents may flow in the rectifier 217and/or the DC link 218 even when the load 202 is operating under normalconditions. For example, when the electrical apparatus 210 is connectedto a "stiff grid," excessive and damaging or potentially damagingcurrents may flow in the rectifier 217 and/or the DC link 218 even whenthe load 202 is operating under normal conditions. Thus, by analyzingthe frequency content of the input voltages at input nodes 214 a, 214 b,214 c, the control system 230 is able to detect the presence of damagingor potentially damaging currents even when the load 202 is operatingunder normal conditions. Moreover, the control system 230 is able todetect the presence of damaging or potentially currents in the rectifier217 and/or DC link 218 that may arise when an unbalanced voltagecondition exists.

To determine whether a performance condition exists, in someimplementations, the property or properties of the frequency contentdetermined in (530) are compared to a specification. The specificationincludes one or more values that are associated with performanceconditions of the electrical apparatus 210. For example, thespecification may include a range of amplitude values for the fifthharmonic of an input voltage frequency signal that are correlated withsatisfactory or safe operation of the rectifier 217 and the DC link 218.In this example, an amplitude of the fifth harmonic is determined frommeasured data (the frequency domain input voltage signals Vfa, Vfb, Vfc)and compared to the specification. If the determined amplitude is withinthe specification, then a performance condition does not exist based onthat criteria (the amplitude of the 5^(th) harmonic in this example). Ifthe determined amplitude is outside of the specification, then aperformance condition exists based on that criteria. The specificationmay include one or more values or criteria that are specific to eachCategory 1, 2, 3.

To provide a more specific example, the electrical apparatus 210 may bein Category 1 (a balanced condition). In this example, the specificationindicates that, if the amplitude of the 5^(th) harmonic in the inputvoltage frequency spectrum is greater than or equal to 5 V, then aperformance condition does not exist. If the determined amplitude of the5^(th) harmonic is less than 5 V, then a performance condition exists.Because the input voltages are known to be balanced in this example, insome implementations, the amplitude of the 5^(th) harmonic of only oneof the phases (Vfa, Vfb, or Vfc) is compared to the threshold todetermine whether a performance condition exists. In someimplementations, the amplitude of the 5^(th) harmonic in all phases(Vfa, Vfb, and Vfc) are compared to the 5V threshold even though theamplitude of the 5^(th) harmonic should be the same in each phase in aCategory 1 or balanced scenario.

The specification may include different thresholds for Category 1, 2,and 3 as discussed by way of the following examples. The Category inwhich the electrical apparatus 210 operates may be determined in (515)as discussed above. In implementations in which (515) is not performedand the unbalanced metric is not determined, the electrical apparatus210 is assumed to be balanced and operating in Category 1.

The specification may be implemented as a database or lookup table thatstores thresholds in association with Category 1, Category 2, and/orCategory 3. The example discussed above related to the amplitude of the5^(th) harmonic voltage spectrum relates to the electrical apparatus 210being in Category 1. In another example, the electrical apparatus 210 isin Category 2 (unbalanced condition but not single-phase). In thisexample, the specification includes a threshold value for the amplitudeof the 5^(th) harmonic of the voltage frequency spectrum in each phasea, b, c. In other words, the amplitude of the 5^(th) harmonic isextracted from each of Vfa, Vfb, Vfc, and each of these extractedamplitudes is compared to a separate threshold. The separate thresholdsmay all have the same value or they all may have different values. Forexample, the separate thresholds may all be 5 V, or the separatethresholds may each have a different value. In these implementations,the electronic storage 232 includes logic or instructions that declarethat a performance condition exists if the amplitude of the harmonic ofinterest (the 5^(th) in this example) is less than the threshold forthat phase. For example, a performance condition may be declared toexist if two of Vfa, Vfb, Vfc have an amplitude of the harmonic ofinterest that is less than the threshold for the associated phase.

Moreover, the specification may store different thresholds that areapplicable to single-phase operation (Category 3). In single-phaseoperation, all of the current in the electrical apparatus flows throughtwo of the input nodes 214 a, 214 b, 214 c. Thus, the amplitudes of theharmonics of the voltage spectrum for two of the signals Vfa, Vfb, Vfcare very low (indicating very high current flow in the case of a "stiffgrid"), or relatively high (indicating the case of a "weak grid"), andthe amplitude of the harmonics of the third phase voltage spectrum iszero, since there is no current flowing in that phase. In this example,the specification may include a threshold that indicates if the systemis a stiff grid or a weak grid. The amplitude of the harmonic ofinterest in each of Vfa, Vfb, Vfc is compared to the threshold and aperformance condition is declared or not declared based on the outcome.

The example above discusses a threshold that is a single value (forexample, 5 V) associated with a single harmonic in the voltage spectrum.However, the specification may include thresholds that include manyvalues or many ranges of values, each of which is associated with adifferent criteria. For example, the specification may include a rangeof values that each represent acceptable amplitudes for one of aplurality of harmonic components. The specification may include a rangeof values that represent an acceptable amount of THD. Furthermore, thespecification may include ranges of values that represent unacceptableamount of a particular criterion.

Furthermore, more than one criterion may be used to determine whetherthe performance condition exists. For example, the amplitudes for thefifth, seventh, eleventh, and/or or thirteenth harmonics may beproperties of the frequency content. Each of these harmonics may becompared to a threshold value associated with that harmonic. If two ofthe three harmonics exceed their threshold but one does not exceed thethreshold, a performance condition may still be deemed to exist. Forexample, the electronic storage 234 may store rules that indicate thatif a majority of determined harmonics exceed the respective threshold inone or more phases, then a performance condition exists. Furthermore,the rules may include specific rules for each of the Categories 1, 2,and 3. Using more than one criteria may enhance the accuracy of theprocess 500, avoid false alarms, and improve the overall performance ofthe system 200.

The specification is stored on the electronic storage 234. The valuesthat are associated with the criterion or criteria that collectivelymake up the specification may be entered by the manufacturer at the timeof assembling and programming the control system 230. For example, themanufacturer may test the electrical apparatus 210 under variousconditions and determine the values for the specification based on thetest results. The various conditions include connection to powerdistribution networks of different SCCR. For example, the specificationmay include various thresholds that are each based on test resultsobtained while the electrical apparatus 210 is connected to a 100 kAnetwork, a 5 kA network, a 20 kA network, and a 50 kA network. Thespecification alternatively or additionally may include thresholds thatare based on high input currents that may flow in one or more of theinput nodes 214 a, 214 b, 214 c when the electrical apparatus 210 has avoltage imbalance.

The manufacturer may use the same values for all electrical apparatusesof a particular type (for example, all VFDs or UPS of a particularmodel) at a particular load, or the electrical apparatus 210 may beindividually tested with a known load. In some implementations, thespecification is updated during the lifetime of the electrical apparatus210. For example, the control system 230 may be configured to permit theoperator to add new values and/or new criteria to the specificationthrough the I/O interface 236, or the manufacturer may push updates tothe control system 230.

Furthermore, in some implementations, the frequency-based properties ofone phase are compared to the same frequency-based properties of theother phases. For example, if an unbalanced condition exists based on(515), the frequency content of each phase is different and thefrequency-based properties are also different. Thus, when an unbalancedcondition exists, comparing the same frequency-based property amongdifferent phases provides more information about the condition of theelectrical apparatus 210. In these implementations, the frequency-basedproperties of each phase also may be compared to the specification.

If a performance condition exists, a flag or other indication may bestored on the electronic storage 234.

The control system 230 assesses whether a performance condition exists(550) based on the determination made in (540). For example, the controlsystem 230 may determine whether or not a flag was set in (540). If aperformance condition does not exist, the process returns to (510) andcontinues to perform (510)-(540) during operation of the electricalapparatus 210. If a performance condition exists, then the controlsystem determines whether or not the load 202 on the electricalapparatus 210 may be reduced (560). Reducing the load 202 on theelectrical apparatus 210 results in the input currents ia, ib, ic beinglower and thus reduces the stress on the components in the rectifier 217and DC link 218. Thus, reducing the load 202 on the electrical apparatus210 may correct or compensate for the performance condition.

Whether or not the load 202 on the electrical apparatus 210 may bereduced depends on the application that uses the electrical apparatus210 and the nature of the load 202. For example, the load 202 may be athree-phase motor that drives a fan for a heating and ventilationsystem. In these implementations, the load 202 may be reduced byreducing the speed of the motor, which reduces the speed of the fan.Reducing the speed of the motor by a small amount may impact theperformance of the heating and ventilation system (by reducing the speedof the fan) but is unlikely to cause the heating and ventilation systemto malfunction or shut down. In another example, the load 202 may againbe a motor, but the motor is used to move a portion of a fast-movingconveyor belt. Reducing the load 202 would reduce the speed of themotor, and is not practicable in this scenario.

Information related to whether or not the load 202 may be reduced may bestored on the electronic storage 234, and the control system 230determines whether or not to reduce the load 202 based on theinformation. For example, the operator may specify that the load 202 maybe reduced or may not be reduced. In other implementations, themanufacturer may program the control system with a list of possibleapplications and associate each possible application with an indicationof whether or not the load 202 may be reduced. The operator is able toselect the application from a menu presented at the I/O interface 236.In these implementations, the control system 230 determines whether ornot to reduce the load 202 based on the preprogrammed setting for theoperator's application.

If the load may be reduced, the control system 230 reduces the load 202(570). The load 202 may be reduced by, for example, reducing the currentand/or voltage provided to the load 202. Moreover, if the load 202 isreduced at (570), the control system 230 may increment a counter thattracks how often the load 202 has been reduced. The process then returnsto (510). The process 500 thus continues to monitor the input voltagesat the input nodes 214 a, 214 b, 214 c. If the load reduction wasinsufficient to correct the performance condition, and the counterindicates that the load 202 has been reduced previously, the controlsystem 230 may determine that the load 202 cannot be reduced at (560).

If the load 202 may not be reduced, the control system 230 disconnectsthe electrical apparatus 210 from the distribution network 201. Forexample, the control system 230 may switch off the inverter 219 or causea fuse between the input nodes 214 a, 214 b, 214 c and the distributionnetwork 201 to operate.

Accordingly, control system 230 is capable of determining whetherpotentially damaging situations (such as overcurrent) that may occurwhen the electrical apparatus 210 is used in a typical situation inwhich the voltage inputs are balanced, and the control system 230 alsois capable of determining whether a potentially damaging overcurrentsituation related to an unbalanced condition (such as a single-phasecondition) exists.

Other implementations are within the scope of the claims. For example,the rectifier 217 is shown as a 6 \-diode rectifier. However, otherimplementations are possible. For example, the rectifier 217 may be madewith 12 or 18 diodes. The process 500 is discussed in the context of athree-phase system, but may be used in a single-phase application or maybe used to analyze a single phase of a multi-phase system.

1. A control system configured to: receive a plurality of input signals,each input signal representing a voltage at one input node of athree-phase electrical apparatus; determine an unbalance metric bycomparing the plurality of input signals to each other; determine abalance property of the three-phase electrical apparatus based on theunbalance metric, wherein the balance property indicates whether thethree-phase electrical apparatus is operating in a balanced condition,an unbalanced condition, or a single-phase condition; and determinewhether a performance condition exists in the three-phase electricalapparatus based on frequency content of one or more of the plurality ofinput signals.
 2. The control system of claim 1, wherein the controlsystem is further configured to access a specification that includes afirst criteria associated with a balanced condition, a second criteriaassociated with an unbalanced condition, and a third criteria associatedwith a single-phase condition; and to determine whether a performancecondition exists, the control system is configured to compare thefrequency content to one of the first criteria, the second criteria, orthe third criteria depending on the determined balance property.
 3. Thecontrol system of claim 1, wherein, if a performance condition exists inthe three-phase electrical apparatus, the control system is configuredto issue a command to the three-phase electrical apparatus to reduce anamount of power provided to a load that is electrically connected to thethree-phase electrical apparatus.
 4. The control system of claim 1,wherein, if a performance condition exists in the three-phase electricalapparatus, the control system is configured to issue a command todisconnect the three-phase electrical apparatus from the electricalpower distribution network.
 5. The control system of claim 1, whereinthe determined frequency content comprises one or more harmoniccomponents of the voltage signal, the control system is furtherconfigured to determine a property of the frequency content, and thecontrol system determines whether the performance condition exists basedon the property; and the property of the frequency content comprises anamplitude of the one or more harmonic components of the voltage signal.6. The control system of claim 1, wherein the unbalanced metric is anunbalance percentage.
 7. The control system of claim 6, wherein theunbalanced percentage is determined based on a difference between theamplitude of the voltage at one input nodes of the three-phaseelectrical apparatus and an average amplitude of the voltages at all ofthe input nodes of the three-phase electrical apparatus.
 8. The controlsystem of claim 2, wherein the frequency content comprises an amplitudeof one or more harmonics of the voltage of at least one input node. 9.The control system of claim 1, wherein, when the balance propertyindicates that the three-phase electrical apparatus is operating in abalanced condition, the control system is configured to determinewhether a performance condition exists based on the frequency content ofonly one of the plurality of input signals.
 10. The control system ofclaim 1, wherein, when the balance property indicates that thethree-phase electrical apparatus is operating in an unbalanced conditionor a single-phase condition, the control system is configured todetermine whether a performance condition exists based on the frequencycontent of more than one of the plurality of input signals.
 11. A methodcomprising: accessing a plurality of input signals, each input signalrepresenting a voltage at one input node of a three-phase electricalapparatus; analyzing the plurality of input signals to determine whetheran unbalanced condition exists in the three-phase electrical apparatus;determining an unbalanced metric of the three-phase electricalapparatus; determining a balance property of the three-phase electricalapparatus based on the unbalanced metric, wherein the balance propertyindicates whether the three-phase electrical apparatus is operating in abalanced condition or unbalanced condition; and determining whether aperformance condition exists in the three-phase electrical apparatusbased on frequency content of one or more of the input signals and thebalance property.
 12. The method of claim 11, wherein the balanceproperty further indicates whether the three-phase electrical apparatusis in a single-phase condition.
 13. The method of claim 12, whereindetermining whether a performance condition exists comprises: accessinga specification that includes a first criteria associated with abalanced condition, a second criteria associated with an unbalancedcondition, and a third criteria associated with a single-phasecondition; and comparing the frequency content to one of the firstcriteria, the second criteria, or the third criteria depending on thedetermined balance property.
 14. The method of claim 11, whereindetermining the unbalanced metric comprises determining a quantity thatcharacterizes a discrepancy of among the voltages at the input nodes asa function of time.
 15. A system comprising: an electrical apparatuscomprising: a plurality of input nodes, each input node configured toelectrically connect to a phase of an alternating-current (AC)electrical power distribution network; and an electrical networkelectrically connected to the input nodes; and a control systemconfigured to: receive a plurality of input signals, each input signalrepresenting a voltage at one input node of the electrical apparatus;determine an unbalance metric by comparing the plurality of inputsignals to each other; determine a balance property of the electricalapparatus based on the unbalance metric, wherein the balance propertyindicates whether the electrical apparatus is operating in a balancedcondition or an unbalanced condition; and determine whether aperformance condition exists in the electrical apparatus based onfrequency content of one or more of the plurality of input signals andthe balance condition.
 16. The system of claim 15, wherein theelectrical apparatus further comprises: an impedance network comprisinga plurality of impedances, each impedance electrically connected betweenone of the plurality of input nodes and ground; and the electricalnetwork comprises: a rectifier; an inverter; and a capacitive networkbetween the rectifier and the inverter.
 17. The system of claim 16,wherein the balance property further indicates whether the three-phaseelectrical apparatus is in a single-phase condition.
 18. The system ofclaim 17, wherein the control system is further configured to access aspecification that includes a first criteria associated with a balancedcondition, a second criteria associated with an unbalanced condition,and a third criteria associated with a single-phase condition; and todetermine whether a performance condition exists, the control system isconfigured to compare the frequency content to one of the firstcriteria, the second criteria, or the third criteria depending on thedetermined balance property.
 19. The system of claim 15, wherein, if aperformance condition exists in the electrical apparatus, the controlsystem is configured to issue a command to the electrical apparatus toreduce an amount of power provided to a load that is electricallyconnected to the electrical apparatus.
 20. The system of claim 15,wherein, if a performance condition exists in the electrical apparatus,the control system is configured to issue a command to disconnect theelectrical apparatus from the electrical power distribution network.